Lesson 2: T-test

• The t-test is a statistical test procedure that tests whether there is a significant difference between the means of two groups.
• There are three different types of t-tests:

  1. one sample t-test
  2. independent-sample t-test
  3. paired-sample t-test
• We use the one sample t-test when we want to compare the mean of a sample with a known reference mean.
• A manufacturer of chocolate bars claims that its chocolate bars weigh 50 grams on average. To verify this, a sample of 30 bars is taken and weighed. The mean value of this sample is 48 grams. We can now perform a one sample t-test to see if the mean of 48 grams is significantly different from the claimed 50 grams.
• We use the t-test for independent samples when we want to compare the means of two independent groups or samples. We want to know if there is a significant difference between these means.
• We would like to compare the effectiveness of two painkillers, drug A and drug B. To do this, we randomly divide 60 test subjects into two groups. The first group receives drug A, the second group receives drug B. With an independent t-test we can now test whether there is a significant difference in pain relief between the two drugs.
• The t-test for dependent samples is used to compare the means of two dependent groups.
• We want to know how effective a diet is. To do this, we weigh 30 people before the diet and exactly the same people after the diet. Now we can see for each person how big the weight difference is between before and after. With a dependent t-test we can now check whether there is a significant difference.
• Identify the three different types of t-tests.

  A) independent samples t-test

  B) one sample t-test

  C) paired samples t-test

  
• To calculate the t-value, we need the t-value or  the difference of the means the and the standard deviation from the mean.
• In calculating the t value:

  A) difference between mean values

  B) standard deviation from the mean

  C) standard error

  
• In the one sample t-test, we calculate the difference between the sample mean and the known reference mean. s is the standard deviation of the data collected and n is the number of cases. s divided by the square root of n is then the standard deviation from the mean or the standard error.
• One sample t-test

  A) mean

  B) reference

  C) standard deviation

  D) number

  
• In the t-test for independent samples, the difference is simply calculated from the difference of the two sample means. To calculate the standard error, we need the standard deviation and the number of cases of the first and the second sample.
• Independent samples t-test

  A) mean

  B) mean

  C) standard deviation

  D) number

  
• In the paired samples t-test, we only need to calculate the difference of the paired values and calculate the mean from this. The standard error is then the same as in the t-test for one sample.
• Paired samples t-test

  A) mean

  B) standard deviation

  C) number

  
• The paired sample t-test is very similar to the one sample t-test.
• No matter what t-test we calculate, the t-value will be greater if we have a greater difference between the means.
• No matter what t-test we calculate, the t-value will be smaller if we have a smaller difference between the means.
• The t-value will be smaller if we have a larger dispersion of the mean.
• The more scattered the data, the less meaningful a given mean difference is.
• We use the t-test to determine if we can reject the null hypothesis or not.
• To use the t-test, we use the t-value in two ways:

  A) critical t-value

  B) p-value

  
• The p-value tells us how likely we would draw a sample that deviates from the population by the same amount or more than the sample we drew. Thus, the more the sample deviates from the null hypothesis, the smaller the p-value becomes.
• Significance level refers to the border of what point we can reject the null hypothesis.
• Significance level is usually set at 5%.
• If the significance level is set to 5%, it means that you are 95% sure that you will test the correct hypothesis.
• In the one sample t-test and the paired sample t-test, the degrees of freedom are the number of cases minus one.
• In the independent samples t-test, the degrees of freedom is calculated by adding the number of people from both samples and minus it by 2 since we have two samples.
• If our calculated t-value is greater than the critical t-value, we reject the null hypothesis.
•  If the p-value is smaller than the significance level, we reject the null

  hypothesis in this way.